the matching operators work against the $_ default variable, unless otherwise specified. The easiest thing to do here is to load that variable with he contents that you want to search, preferably within a local block:

my $url = undef;
local{
  $_ = $mech->content; #not sure if mech let's you do  
                       #this...basically you want to load
                       #the $_ var with the data that holds
                       #the url
  m{<strong.*?(http://.*?)&};
  $url = $1;
}
print $url;
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