I think a slightly simpler approach is to regex directly on the strings, combine the strings and then dedup:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

my @array = ("11 12","11 13", "9 8 7", "3 4", "11 4") ;

## combine
AGAIN: for my $i ( 0 .. $#array ) {
    for my $j ( 0 .. $#array ) {
        next if $i == $j;
        while( $array[ $j ] =~ m[(\d+)]g ) {
            my $n = $1;
            if( $array[ $i ] =~ m[\b$n\b] ) {
                $array[ $i ] .= ' ' . splice @array, $j, 1;
                goto AGAIN;
            }
        }
    }
}
## dedup
for ( @array ) {
    1 while s[(\b\d+)(?:\s|$)(?=.+\1)][]g;
}

pp \@array;

__END__
c:\test>897418
["12 13 11 3 4", "9 8 7"]
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