X is number of coin flips needed to get m tails OR m heads. What is the cumulative distribution function of x?

m is an arbitrary natural number. I tried with this formula $$\sum_{k=m}^{x}{ {k-1} \choose m-1}*2^{1-k} $$ and mathematica gives an answer, but I need the procedure how to get to that on paper.
Thanks

Probability
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