You are just wanting to push the value onto the appropriately dereferenced list.

push @{$arr[1][1]}, 222;
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As with some of the other comments, the declaration of the structure leads me to believe that the OP was trying to specify a hash of lists. e.g.

my %hoa=("one" => [1,11], "two"=> [2,22]);
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in which case

push @{$hoa{two}}, 222;
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