There are many reasons to upgrade, mainly Obsolescence.
QC11 is OUT OF SUPPORT (no more patches), 11.52 soon to go out of support.
It is also likely that your QC11 is on a Win2003 server, which is out of support by MS. You may also have SQL-Server prior to SQL2008, which will soon be out of support by MS if not already. You might be on an old version of Oracle 10g or 11g, which is getting old.
Operating on these older environments are just asking for trouble. disaster will strike eventually and there will be nowhere to turn for help since everything is out of date.
When upgrading, you will need a NEW QC server running Win2008R2 or later, as well as SQL-server 2012 or newer.
You can migrate your QC projects and repository to the new environment and upgrade them.
Now, since you have QC11, it will first need to be upgraded (qcsiteadmin_db AND projects) to QC11.52.
Then, we Suggest that you will need to upgrade qcsiteadmin_db first to 12.21, then to 12.5x as we have seen issues going straight to 12.55 from 11.52.
In the install guide for 12.55 specifically mentions upgrade path for PROJECTS allowed from 11.52 to 12.55 directly, so perhaps there are only issues with qcsiteadmin upgrade on some installations.
Another big reason is that the newer version(s) of QC/ALM software are FREE to customers on MicroFocus approved maintenance/support.
Also, if you are on support, they WILL take cases related to the upgrade process from an out of support QC version to an IN-support version.