If $\displaystyle \sqrt{{{x}}}+\sqrt{{{y}}}={11}$ and $\displaystyle {y}{\left({9}\right)}={64}$, find $\displaystyle \frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}{\mid}_{{{x}={9}}}$ by implicit differentiation.

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