# Maximum sum power of cubic

Algebra Level 5

$\large{ \begin{cases} a+b+c+d+e+f=6 \\ a^2+b^2+c^2+d^2+e^2+f^2=\frac{36}5 \end{cases}}$

Let $$a,b,c,d,e$$ and $$f$$ be positive real numbers such that the system of equations above are fulfilled. If the maximum value of

$a^3+b^3+c^3+d^3+e^3 + f^3$

can be expressed as $$\dfrac xy$$ for coprime positive integers $$x$$ and $$y$$, find the value of $$\sqrt{x+y}$$.

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