The specification is still vague. What should the third value be if it's not the same, e.g. [0, 5, 1] and [0, 5, 2]? Also, in what order should the triplets be printed?

The following code uses the order of the first appearance of the first two columns, and uses the third value from the first occurrence.

Update: The %seen hash contains the index into the @out array, i.e. the index of the first occurrence of the two values.

#!/usr/bin/perl
use strict;
use feature qw{ say };
use warnings;

my %seen;
my @out;
while (<DATA>) {
    my @n = /-?[0-9]+/g;
    if ($n[0] == 0 || $n[1] == 0) {
        if (exists $seen{"@n[0, 1]"}) {
            $out[ $seen{"@n[0, 1]"} ][$_] += $n[$_] for 0, 1;
        } else {
            push @out, \@n;
            $seen{"@n[0, 1]"} = $#out;
        }
    } else {
        push @out, \@n;
    }
}

say "[@$_]" for @out;

__DATA__
[ -1, 5, 1 ],
[ 0, 5, 1 ],
[ 0, 5, 1 ],
[ 1, 5, 1 ],
[ 3, 4, 1 ],
[ 5, 1, 1 ],
[ 5, 0, 1 ],
[ 5, 0, 1 ],
[ 5, 0, 1 ],
[ 5, 0, 1 ],
[ 5, 0, 1 ],
[ 5, 0, 1 ],
[ 0, -5, 1 ],
[ 0, -5, 1 ],
[ 0, -5, 1 ],
[ 0, -5, 1 ],
[ 0, -5, 1 ],
[ 0, -5, 1 ],
[ 0, -5, 1 ],
[ 0, -5, 1 ],
[ 0, -5, 1 ],
[ -23, -64, 0 ],
[ -5, 0, 1 ],
[ -5, 1, 1 ],
[download]

Output:

[-1 5 1]
[0 10 1]
[1 5 1]
[3 4 1]
[5 1 1]
[30 0 1]
[0 -45 1]
[-23 -64 0]
[-5 0 1]
[-5 1 1]
[download]