That's different RAM you're referring to. The 350 MB of free RAM is from the System RAM (I think 1GB on the XOOM), which is used for active apps and processes. This is the RAM that Android likes to keep relatively full with processes in order to keep them active and swap between them more efficiently. Your XOOM otherwise has at least 8 GB of storage space to install apps (i.e., if you have the 16 GB version).
The 110 MB of free memory that the OP is referring to sounds like the Application Storage, which is separate from system RAM, and which is where apps are stored when installed. That is an exceedingly low amount of available memory. The only thing you can do if you don't want to root the phone is to go through each app under Settings/Apps, and move as many of them as you can to Internal Storage (that's the onboard RAM that's partitioned into a separate storage section, sometimes confusingly referred to as SD card--not to be confused with the external SD card that you physically insert).
You could also try App2SD, which can move apps to an external SD card, but from what I know, it only works on Gingerbread and below; so if you have Android 4 and above, it won't work.