# Squares In Between

$\begin{cases} a + b + c = 11\\ a^3 + b^3 + c^3 = 785 \end{cases}$

If $$a, b, c$$ are the integers, whose sum of any two variables is larger than 1, that satisfy the system above, what is the value of $$a^2 + b^2 + c^2$$?

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