Your 9 speed hub will probably not be able to accept an 11 speed cassette- it's too wide.
You can upgrade to 10 speed 5600/5700/6600/6700 with just a new cassette and shifters. You can change the RD if you really want to, but not necessary.
In any case, neither an upgrade to 10 speed nor the more expensive change to 11 speed would necessarily make you any faster. Definitely better shifting feel and feedback, but that's about it. If you're in a place where the bike is actually holding you back (e.g. weight, wheels) then you would be better off saving up for a new bike.
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