Suppose that some real number x satisfies
\log _{2} x+\log _{8} x+\log _{64} x=\log _{x} 2+\log _{x} 16+\log _{x} 128
Given that the value of \log _{2} x+\log _{x} 2 can be expressed as \frac{a \sqrt{b}}{c}, where a and c are coprime and b is squarefree, compute a b c.