Ok, try this. As normal user (not root) type
This will show you what groups your normal user is a part of.
Now, try this, again as a normal user:
This file will show you the groups structure on your machine. There most likely is one called 'cdrom'
On an ubuntu machine, you do the following to add a user to a group:
sudo adduser <user> <group>
It's a long time since I worked with Fedora, can't remember exactly how to add user to group, but search on this forum.