@eeeee for what it's worth, it's internal policy in NodeBB that nvm and n NEVER be installed on our client machines.
It's caused far too much headache for this very same reason. I think I have gone as far as to migrate an entire client site to another server just to get back to a node version I could control. It was rather cathartic to send the old server to /dev/null.
Anyway, the problem here is as @phenomlab pointed out, is path related. Both n and nvm fmuck around with the symlinks in /usr/bin or /bin, etc., and there's no easy way to undo what those scripts do unless you run the uninstallation script.
How do you know which uninstall script to run? You don't. Did you use nvm or n, and if so, which one? Who knows now. If you do know, does the script provide information (via --help flag or whatnot) to instruct you on how to uninstall it? Ha ha, of course not.
Let me have apt control my dependencies any day. Warts and all. Rant over.