i have sympathy for you, smudge, as difficult children are a nightmare and do send you insane fairly quickly! it sounds like you may have made a rod for your own back by giving in in the past or accommodating her due to home circumstances (i.e. during divorce/seperation, new relationship and siblings etc.). so, now it is time for tough love. that includes being firm, consistent and laying down new rules for behaviour - and punishing her if she does not behave well. she is 11, so is capable of not being a brat if she wants to.
smacking and shouting do not work (and only foster nasty thoughts/feelings in the child!) so you will have to think of other ways like no pocket money, no treats, no time/attention when she behaves badly (positive praise and attention should be given when she behaves appropriately) and maybe removing things from her room that she values (like the tv etc. - my mum did this to me and it drove me nuts but made me behave myself).
your daughter will resist and play up at first to continue to try and get her own way, but explain to her what is happening, be firm and consistent - and if you have a paartner, they must also sing off the same song sheet too and back you all the way. at the end of the day, you are the adult - assert your authority and look like you mean it. new, firm but fair mummy must be in charge! good luck (and it is lots of work, but worth it in the long run!) x