HP Sprinter 11.52 supports HP Application Lifecycle Management (QC) 11.00 (with ALM Patch 12 or later). You can utilize Sprinter 11.52 if your QC server is patched to 12 and up, you don't have to be limited to just Sprinter 11.0.
You say though you have Sprinter 11.0 installed now but have some issues. To troubleshoot this, here are a few things to check.
1. Ensure you have patch 09 installed for Sprinter 11. Patch 09 is required for proper performance and connection to QC.
2. Ensure the HP Connectivity add-in is installed (this is to let Sprinter allow a user to login to QC)
3. Is QTP installed? Or UFT? I ask as Sprinter 11.0 and QTP 11.0 are compatible on the same machine, but UFT and Sprinter 11.0 are not. Also there are some patches required for QTP and QTP has to be installed first prior to Sprinter being installed.