Something along these lines should do the job I think:

#!/usr/bin/perl

use strict;
use File::Find;

my @dirs = @ARGV or die "Please supply a valid directory to search";

find(\&wanted, @dirs);
sub wanted{
  if(-f && m/\.(mp3|rm)$/){ print "$File::Find::name\n"; }
}
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Update: Thanks to andreas1234567 for suggesting I add a -f test to avoid printing non-files. I guess, it's unlikely to find anything other than a file that ends ".mp3" or ".rm", but best to be on the safe side!