If you're anything like me, it didn't work for me either. I added a last line:

else {
  print $mech->content
}
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... and got the following output:

LWP will support https URLs if the Crypt::SSLeay module is installed.
More information at <http://www.linpro.no/lwp/libwww-perl/README.SSL>.
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Try going there, reading that, and installing Crypt::SSLeay.

s**lil*;  $*=join'',sort split q**;  s;.*;grr; &&s+(.(.)).+$2$1+; $; =
qq-$_-;s,.*,ahc,;$,.=chop for split q,,,reverse;print for($,,$;,$*,$/)
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Yep. I should've used autocheck => 1 in WWW::Mechanize->new's parameters; that would've reported it.

autocheck => 1 is a good idea anyway.