Dashboard does not render after updating civi version 4.6.9 to 4.6.10 and onwards to 4.6.11
sounds like a cashing problem. 
Not showing up dashlets usually can have 2 causes:


Settings are wrong:


Administer -> System Settings -> Directories
Administer -> System Settings -> Resource URL's
Administer -> System Settings -> Cleanup Caches and Update Paths 

Cache files


Because it used to work in 4.6.9 I would guess "Cache Files".

Remove cache via 
Administer -> System Settings -> Cleanup Caches and Update Paths
and remove files in JOOMLA_ROOT/media/civicrm/templates_c/