Find \[ \large\displaystyle\sum_{k=1}^{n} \left (x_{k} \right ) \]

where : \( n\)= number of values of \(x\) in equation :

\( x^{[(\frac{3}{4})(\log_{2}x)^{2}+\log_{2}x-\frac{5}{4}]} = \sqrt{2} \).

If your answer come as \( \frac{ a+b\sqrt[c]{d}}{d} \) submit it as \( a+b+c+d \).

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