The official end of life for the product and support of ALM 11.0 was January 2015. We would recommend that you upgrade to the current latest version (which at this time is ALM 12.55). However you will need to assess your environment needs and availability to decide what would be the best route for your organization. ALM 12.55 will require many environment upgrades from your current environment for the application host, however this will provide you with the latest version for the greatest longevity and support of all the current versions. The environment variables supported can be found here: https://admhelp.microfocus.com/alm/specs/alm-qc-system-requirements.htm#ALM1250
As for your upgrade, no matter the current ALM 12.x version being upgraded to, you will have to perform a multiple part upgrade as there is no direct route from ALM 11.0 version to any ALM 12.x version. You will need to upgrade your version and products to the intermediary version of ALM11.52 first and then continue the upgrade path to the ALM 12.x version of your choosing (once again I would recommend ALM 12.55 patch 2 as it is the latest at this time). I would recommend that you stand up an ALM 11.52 version and ALM 12.55 version at the same time as your current ALM 11.0 version is still active so that you may upgrade the projects in stages and provide for the greatest availability of the projects and the most efficient and less evasive upgrade/ migration while keeping production available for your users (if only for certain projects, but some productivity is better than none and having your users sitting idle).
Hope this helps in determining what works best for your corporation and situation,