Figure of 11000 years, is likely a case of bad translation.
Following is the verse, which is not specified in the Qn:
दशवर्षसहस्राणि दशवर्षशतानि च । रामो राज्यमुपासित्वा ब्रह्मलोकं प्रयास्यति ।। [source]
In Sanskrit the word "सहस्र / Sahastra" is translated as "many/several" or "thousand". An accurate number like "thousand" is least likely to be the right word for such verses.
However, some people would strictly translate as following:
दशवर्षसहस्राणि = 10 thousand years
दशवर्षशतानि = 10 hundred years
Total = 10000 + 1000 = 11000 years!
This is not only irrational, but is also not sensible even from Ramayana perspective itself.
- Archaeology: As per recent survey, RAmAyana happened 7000 years back (i.e. killing of RAvana). In that sense, RAma must be living till now!
- RAmAyana: Just imagine if the ages were 10000 years, then would Kaikeyi make RAma to exile for just 14 years!? 14 years in 10000 years is as good as 51 days in 100 years. :-)
So here is more sensible interpretation:
After serving the kingdom for several decades and ten years after [the age of] hundred, RAma proceeded towards Brahmaloka (highest of all planes).
So RAma's life span can be 110+/- years. During that, he ruled the kingdom for few decades (5-7).
Here is another misinterpretation of Dasaratha's age depicted as 60000 years!
षष्टिः वर्ष सहस्राणि जातस्य मम कौशिक ... [Valmiki Ramayana- Verse-10]
Sixty thousand years have passed from my birth, ...
In 60000 years, 14 years of exile of RAma would have felt like 9 days! It's unbelievable, that Dasharatha would have died in grief of just short span!
Now here is how one should interpret:
षष्टिः = 60
सहस्र = many or several (not thousand)
 Six decades of years have passed from my birth, ...
 As many as Sixty years have passed from my birth, ...
Refer this post for some more information on the same topic.