If you care about the things that Wii U Browser Exploit can offer you, then you must stay on v5.1.0
Big 'N' has pulled out their coders and blocked all known Webkit Browser Exploits with their latest firmware v5.1.1 just released for the Nintendo Wii U
It has only been a week since MarioNumber1 updated the v4.x codebase of the released Wii U Browser Exploit, to be able to handle the latest v5.0.0 and v5.1.0 updates from Nintendo.
But those cheers of having online cheats, homebrew and dumping needed keys from your Wii U console was short-lived, as now big 'N' has released v5.1.1 and unlike previous updates this one sadly blocks all known WebKit exploits as the codebase has been totally updated, so it the end of road for the Wii U Browser Exploit.
Oh'well, it was fun while it lasted, so if you want to enjoy the things that might be coming in near future you will be forced to NOT UPDATE and leave your Wii U console running on v5.1.0 which for now forces you to be off-line and may prevent newer games.