On here you have various career individuals which is terrific for information sharing, but you need to zero in on your career path and end goal and then focus on how to get from where you are to there. As a current SQA Manager and one who has also been a developer, test engineer, automation engineer, business analyst, deployment/release manager I would offer the following breakdown.
Manual Tester Starting point:
If you just want automation then I would start with a paid tool that does the heavy lifting for you. There are a bunch of them and all have plus/minuses. Here is one site to splinter from http://www.testingtools.com/test-automation/ and also check out the links listed on what-do-i-need-to-start-from-zero-in-automated-testing. The other thing to focus on is html specifically for web apps to understand the rendering of the page as tools read these and it's important to understand how they are being read. This includes things like CSS, HTML, Javascript(references/calls, not the whole thing), SQL, etc...
Going Deeper:
After the above if you want to dig in behind the scenes or utilize a code library like Selenium, then you need to learn coding. Optionally you can also utilize Sikuli http://www.sikuli.org/ which is free but written in a pythonish style and functions on image recognition which makes it easier to utilize than a straight code language approach.
Changing Careers or having a career hobby:
If you want to be a full automation engineer and possibly a developer then start learning code and dive in 100%. Please be aware though that there are multiple full time careers here. Developer, Automation Engineer, SDET engineer, Test/SQA, others similar but variously named. To be a great Test/SQA engineer you don't need to know how to program, but it would set you apart to know how to read code though. The other career paths you need to know how to program with the focus being different. Based on your 11 years of manual testing, I would assume that you want to boost your skills and not swap careers, so I would advise you to focus on how automation tools work and how the applications under test are built and work (html/css/javascript for web and likely unique technologies/libraries utilized and SQL/Oracle as well). Basically don't sit back and only view GUI's but dive into and learn from your counterparts about the specifics of under the hood. If you are in SQA and want to learn more and are surrounded by developers, find the people around you who know what you want to learn and be very curious and eager to learn. Find what they do outside of work to keep skills current and emulate. Immersion is the best way to pick information & skills up and make them your own.