I have an iMac (27-inch, Late 2011) running OS X El Capitan Version 10.11.6. What is the latest OS that I can upgrade to?

Here's the link to more specific High Sierra macOS 10.13.x info

and the mac app store installer file..

• How to upgrade to macOS High Sierra - Apple Support

https://support.apple.com/en-us/HT208969

Check to make sure your applications are compatible.        

Application Compatibility

Also check to make sure there is a compatible driver for your printer.

Do a backup before installing, preferable 2 backups on 2 different drives.

High Sierra. I run that on my early 2011 17 inch MBPro.

I agree with the above

Your 2011 iMac should be able to upgrade to and run macOS 10.13 High Sierra.

Best of Luck to You!