Quadratic in X, Cubic in Y

Number Theory Level 3

$\large \color{green}{X^2+Y^3=793}$ If $$-9 \leq X, Y \leq 9$$ and $$X,Y \in \mathbb{Z}$$ satisfy the above equation, then find the minimum value of $$\color{green}{\left( X+Y \right)}$$.

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