Do not uninstall the 11 version. Install the 9.5 version over it (it will warn you that you are installing an older version, but proceed anyway). If this doesn't work, then I don't know how to help.

Go to the web support center of your PC manufacturer and find the 9.5 version under Intel Management Engine Interface (MEI) drivers for Windows 8.1, 64bit. The driver will work with Windows 10.

I'd like to confirm that downgrading the Intel Management Engine Interface driver to version 9.5 (from version 11.0) solved the problem. My laptop could neither shut down, restart, or wake from sleep...