Uncomment your print ("$dm $dmm");. You'll see that you actually have the literal strings '&date_manip' and '&date_manip1(1)' in them. That's why they're not matching something that looks like a date.

Just use:

$dm = date_manip();
$dmm = date_manip1(1);
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And you'll be a lot closer.

You also may wish to check out Date::Calc and Date::Manip and choose one for your date routines.