Inverse of $f(x)=x+\sin(x)$

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I'm attempting to find $$f^{-1}(x)$$ for the function $$f(x) = x + \sin{x}.$$ So far I've tried some simple algebraic methods as well as rewriting $\sin{x}$ as a power series. I'm not quite sure where to go aside from that. Any direction would be appreciated!