Hi Chandan,
CUE 8.6.6 and later are compatible with CUCM 9.1.x;
Support for Cisco Unified Communications Manager 9.1
Cisco Unity Express 8.6.6 provides support for Cisco Unified Communications Manager 9.1.
http://www.cisco.com/c/en/us/td/docs/voice_ip_comm/unity_exp/rel8_6/rel_notes/rel_notes86.html#pgfId-411381
Because you are moving from a pre-7.1 CUE version you will need to follow the CSL License migration process;
Note
When you upgrade to Cisco Unity Express Release 8.6.x from any release prior to Cisco Unity Express Release 7.1, you must replace your pre-CSL licenses with CSL licenses. You must migrate your licenses for the mailbox features and port features. If you have purchased the optional IVR features, you should also migrate your licenses for the IVR features.
Software Activation for Cisco Unity Express 7.1 and Later Versions
http://www.cisco.com/c/en/us/td/docs/voice_ip_comm/unity_exp/rel7_1/Licensing/CUELicensing_book.html
Cheers!
Rob