I have been able to remove a truss rod nut and replace it with a new one by using a left hand threading tool (only a couple of euros/pounds).
However: if the truss rod nut is worn out, it probably means someone put it under a lot of pressure, so something else might be wrong with it.
There's also https://www.stewmac.com/luthier-tools-and-supplies/tools-by-job/tools-for-truss-rods/stewmac-truss-rod-rescue-tool-sets.html but those are expensive. If you bring it to a luthier who already owns one of those, however, it might be an easy fix.
Best course is probably asking around for a luthier who is experienced in this sort of thing.