The most common issue seen is email reporting unroutable mail domain for any email sent. It appears that in cpanel 11 it requires new ACL's to be placed in the exim.conf. To fix this issue run,
chattr -ia /etc/exim.conf /scripts/buildeximconf /etc/init.d/exim restart
If the problem still continues then there are likely invalid functions in the /etc/exim.conf.local and you can run
mv /etc/exim.conf.local /etc/exim.conf.local.bak
Then run the above commands again.