Simultaneous Equations in Three Variables!

Geometry Level 4

\[\large { \begin{cases} xyz=6 \\ \tan^{-1}(x) + \tan^{-1}(y) + \tan^{-1}(z) = \pi \\ xy+yz+zx = 11 \\ \end{cases} }\]

Let \(x,y,z\) are real numbers satisfy the above equations. Then find the value of \(x^5 + y^5 + z^5 \).

Image Credit: Flickr Francine Vernez.
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