Try: perl -MWWW::Mechanize::Shell -e"shell"

after install and reading the perldoc for WWW::Mechanize::Shell and use the shell to navigate the form, inspect its structure and find a way of submitting that button.

get URL
forms
form FORMNAME
click NAME
   or 
click ""
script 
   (to obtain the results in an executable form 
   for importation into your script)
[download]

-- Hugh