I have tried this with Text::Balanced and it seems to work:

#!/usr/bin/perl
use strict;
use warnings;

use Text::Balanced ':ALL';

while ( my $text = <DATA> )
{
  my @data = extract_multiple( $text, 
         [ \&extract_bracketed, qr/\s+/ ] );
 @data = grep { !/^$/ }
         map {s/^\s+//;s/\s+$//;s/^\(//;s/\)$//;$_}
         @data;
 print join ( '---', @data ), "\n";
}

__END__
A
A B
A B C 
(A B) C
A (B) C
A (B C D)
A(B C D)
A (B C D) E
A (B C D)E
A (B C D) (E F G)
A (B C D) (E F G) I
A B (C (D E) (F G)) (H I)
A B (C (D E) (F G)) (H I) J
A B (C (D E) (F G)) (H I) J K
[download]

because it prints:

A
A---B
A---B---C
A B---C
A---B---C
A---B C D
A---B C D
A---B C D---E
A---B C D---E
A---B C D---E F G
A---B C D---E F G---I
A---B---C (D E) (F G)---H I
A---B---C (D E) (F G)---H I---J
A---B---C (D E) (F G)---H I---J---K
[download]

There is an issue though (perhaps due to my lack of deep knowledge of the module). If I put a line print  $@->{error}, "\n" if $@; after the first line in the loop it prints Did not find opening bracket after prefix: "\s*" every time. Is this something to worry about or just to take note of?

Just my 2 cents.