The correct way is to uninstall 6 before installing 11. That being the case, you might want to try uninstalling both from newest to oldest and then reinstalling 11.
I don't know anything about phone support for a time after purchasing but you can always try the following options and see what you get. These are usually recommended for people who have problems with sewrial numbers or product actiovations, but they might help with other matters (orr they might send you to the product forums)
Here are some links to help make contact:
chat: http://www.adobe.com/support/chat/ivrchat.html
phone: http://www.adobe.com/support/download-install/supportinfo/