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find all functions f: \mathbb{R} \to \mathbb{R} that satisfy the functional equation:
f(x^2 f(x) + f(y)) = (f(x))^3 + f(y), \quad \forall x, y \in \mathbb{R}
f(x^2 f(x) + f(y)) = (f(x))^3 + f(y), \quad \forall x, y \in \mathbb{R}