6.1.1 beta (10B311) does not fix the jailbreak. It’ll probably happen in a future revision. Don’t upgrade though, evasi0n won’t let you jb.
— pod2g (@pod2g) February 7, 2013
iOS 6.1.1 is only available to developers, and does not bring much changes and is not worth updating, except you live in Japan, this update brings improvements to Maps in Japan. However, the Evasi0n will not jailbreak iOS 6.1.1, as pointed out by pod2g, stay away from update if you want to preserve the jailbreak, this is a golden rule.
If you have not upgraded your iDevice to iOS 6.1 we advise you to do so before Apple release iOS 6.1.1, otherwise you will be stuck without jailbreak.