What should I set the environment variable to?

export $PERL_ANYEVENT_NET_TESTS=

Firstly, that's not how to set an environment variable in the shell. The leading dollar should be omitted, eg:

export PERL_ANYEVENT_NET_TESTS=1

See the bash reference for more on using variables in the shell. However that will not solve the test failure. The message about that variable is merely a diagnostic to tell you that a test is being skipped. It is entirely benign.

The tests are actually failling because of

AnyEvent::Handle uncaught error: Connection refused at /root/.cpan/build/AnyEvent-7.12-0C2qsS/blib/lib/AnyEvent/Socket.pm line 1000.

Fix that and you'll be good to go.