If 1x+12x2+14x3+18x4+116x5+⋯=164,\frac{1} {x} + \frac{1} {2x^2} +\frac{1} {4x^3}+\frac{1}{8x^4}+\frac{1}{16x^5}+\cdots=\frac{1} {64}, and xx can be expressed in the form mn\frac{m}{n}, where m,nm,n are relatively prime positive integers, find m+nm+n.

Source: 2011-2012 Winter Online Math Open

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