These paths are not what you think they are, tobyink explains your mistake well.

The first time you run cpan it will explain may things and ask if you want to use local::lib (read the Rationale). With this method you can install modules without root permissions.

A saner alternative is to install your own version of perl there's an automated method (perlbrew) or a manual method, both are fairly trivial, read this post for details.

Update: fixed typo.