This one's a freebie, thanks to Regexp::Common. You can read about using this module to match balanced parens by seeing the docs for Regexp::Common::balanced.

use strict;
use warnings;
use Regexp::Common qw/balanced/;

my $string = '111(22(33)44)55';

$string =~ s/$RE{balanced}{-parens=>'()'}//g;

print $string, "\n";
[download]

You can thank TheDamian and Abigail-II for all the hard work that went into this module.

Note: A regexp solution to matching balanced parens is probably less robust than a proper balanced text parser. For that, you could have a look at Text::Balanced.