The baseband for 3.1.3 is 5.12, not 5.11. 5.11 is from 3.1.2, and if you're running 5.11 on 3.1.3, it's because you upgraded to 3.1.3 by using either sn0wbreeze/PwnageTool.
You just use sn0w/blacksn0w to unlock 5.11. It's that simple.
Seriously, there is no real rush to jailbreak, is there? I upgraded to 3.1.3, and I'm just waiting to jailbreak. Albeit, I've heard that Apple are trying to band people that are jailbroken to access the 'app store'.