This works fine for me:

#!/usr/bin/env perl
use strict;
use warnings;
use LWP::UserAgent;
use HTTP::Cookies;
use Test::More tests => 1;

my $cookie_jar = HTTP::Cookies->new;
my $ua         = LWP::UserAgent->new;

$ua->cookie_jar ($cookie_jar);

my $response = $ua->get ('https://twitter.com/');

like $cookie_jar->as_string, qr/guest_id=/, 'Cookie retrieved';
[download]

HTTP::Cookies 6.01, LWP::UserAgent 6.15.