I have a different solution that might work.
I was unable to mirror my macbook to the apple tv after a timemachine restore, while other devices (iphone, other macs) still were able to mirror their displays. My Airplay icon had simply vanished. Tried resetting router, different ipaddresses, the works but nothing worked. Not even the 1st line apple helpdesk could help me (rebooting computer and clearing caches and stuff).
I have not tried the language trick but my strange solution worked. This seems strange but I downloaded AirServer (trial is free) which turns your own macbook into a Airplay receiver. Suddenly my Airplay icon in the menu bar appeared. I could now mirror to my own Macbook (ricidulous I know) which I did. But then the magic happened: when I got to work today where the Apple TV is, my Airplay icon was showing in the menu bar and I could succesfully mirror again. Really strange but hey, it works 🙂