To go from 10.x to 11.x you'd have to install 11.0 first (or 11.0.01 in some cases) which would uninstall 10 during the process.
There should be no conflict between different versions of Reader and Acrobat 10/11 on the same machine, but there's always the possibility of a bug. Also, an incomplete uninstall of 10 could be the culprit. There's a cleaner tool on LABs.
Ben