$_ = '1()()()2923()())))((';
s/[()]+//g;
print;
[download]

Update: Misread the question and you want to remove using balanced parens: use Regexp::Common::balanced

update2 And there is the solution based on the balanced parens re in perlre i.e.

$string='111(22(33))44554'; 
$re = qr/\((?:(?>[^()+])|(??{$re}))*\)/; 
$string =~ s/$re//; 
print $string
[download]

-enlil