I am sorry that you got your first negative. It sucks, I know.
As to how the cuff links got broken, as I think you already know, it doesn't really matter. It can't be proved one way or the other.
Before you respond to the feedback, reach out to the buyer:
"Dear XXX, I saw the feedback you left about your purchase and I wanted to reach out to better understand what is going on. The photo you provided certainly shows the cuff links broken. They were not in this condition at the time of shipping, so I would like to better understand what happened. Did the cuff links arrive to you in this condition? Was there damage to the box? I look forward to hearing from you so I can issue you a full refund under the proper policy."
Do not ask for any sort of feedback revision at this point. Make your message about the customer, not you. You've put the burden on them to respond and you've dangled a carrot that will hopefully get their attention.
If they respond, great! Win them back over, then, and only then, ask if they would reconsider revising their feedback. If they do change it to a positive, then respond to that and acknowledge there was an issue and that you appreciate them giving you a chance to investigate and refund them. If they do not change their feedback or they do not respond at all to your private message, then a simple response like, "We do not know how the cuff links were damaged, but we did immediately fully refund the buyer when we were alerted to this feedback. We appreciate the opportunity to make things right when something goes wrong."
I am not sure if I totally agree with @mam98031 on this being feedback abuse. My only negative feedback was about 6 months ago. It was a new account and the buyer bought a lot of cheap dollar items. A junk lot basically. Of course the listing had photos of everything in the lot, along with a manifest. Many sellers don't even bother to spell out what is included in these types of lots.
The buyer received it and immediately left negative feedback without reaching out to me. They said something like, "Complete junk. Waste of money." Naturally I was alarmed and reached out to them. I had free returns and I let them know they could return it at my expense. They responded that they had thrown it in the garbage. All of this went down within about two hours of delivery mind you.
I decided to investigate the buyer's account, which is when I noticed it had been created the same day they ordered from me. By looking at the feedback they left others, I discovered they had left 4 other feedbacks, all negative, and all word-for-word like mine. It appeared this buyer had purchased similar junk lots from the other sellers. To me was clear abuse of the feedback system. I appealed to eBay, and they informed it was buyer experience. It was irrelevant how many negative feedbacks the buyer had left or that they all said the same thing. It is what it is.
I did my due diligence and appealed. You certainly have the right to do the same. For me, I like to pick my battles, and now that I know there is at least a chance eBay won't remove feedback due to that reason, I wouldn't bother asking them to. Instead, I'd use that time to list a couple of nice items and try to make sales, so that will lead to positive feedback and boost the overall score up.
Hang in there. I have a close friend who buys a lot from eBay. She isn't concerned about scores unless they are below 98%. If it below that, she will take a few moments to read through to see if there are multiple negative and any common issues.
