I don't have any experience with Ampere, nor high refresh, but I do have quite a lot of experience in commercial installations for digital signage.
Based on that, 5m on (decent quality) copper cables is usually the reliable limit, but anything over that I'd look at fibre-optic based cables.
Just had a look on a well known online purveyor of everything and you can get a 10m for £85, 20m for £90 - reviews on that indicate 1440p@144Hz (so I can't see why 165Hz would be a problem) works fine (on the 20m).
If you have trouble with those, shouldn't be too much hassle to return it!
Hope that helps