Making amx_nextmod, literally or effectively, a public command doesn't make any sense, IMO. Anybody would be able to do it and override anybody else at any time. But you can make the command public if you want to do that. Just set the permissions for that command in cmdaccess.ini.
It make much more sense to have people be able to RTV and then vote on the next mod and then vote on the next map Voting for both the mod and the map is the functionality of Polymorph if poly_mode is set to 2. You can add the RTV functionality with the "Polymorph: Rock the Vote" plugin shown in the second post.