Finding Both Minimum And Maximum

Algebra Level 5

$\large\begin{cases} x+y+z=4\\ x^2+y^2+z^2=6\end{cases}$

If $$x,y$$ and $$z$$ are reals numbers that satisfy the system of equations above, find the sum of the maximum and the minimum value of $$A= x^6+y^6+z^6$$.

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