That happens because you are using the object in ways not documented by the WWW::Mechanize documentation. Please re-read the documentation on ->get and what the method returns. You have the following code:

$page = $mech->get("http://www.google.com");
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This usage is nowhere documented.

Also see the documentation on ->find_link. It shows the following example:

$mech->find_link( n => $number );
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Note how the method is called on a variable named $mech.

Thank you for pointing that out. I understand my mistake. Thank you.