$f(x)=\left\{\begin{array}{1 1}mx^2+m,&x<0\\nx+m,&0 \leq x \leq 1 \\nx^3+m,&x>1 \end{array}\right.$ For what integers $m$ and $n$ does $\lim\limits_{x \to 0} f(x)$ and $\lim\limits_{x \to 1} f(x)$ exist?

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