Evaluating $\lim_{x\to \infty } (x +\sqrt[3]{1-{x^3}} ) $ $$\lim_{x\to \infty } (x +\sqrt[3]{1-{x^3}} ) $$ 
What method should I use to evaluate it. I can't use the  ${a^3}$-${b^3}$ formula because it is positive. I also tried to separate limits and tried  multiplying  with  $\frac {\sqrt[3]{(1-x^3)^2}}{\sqrt[3]{(1-x^3)^2}}$ , but still didn't get an answer. I got -$\infty$, and everytime I am getting $\infty -\infty$ .

I usually suggest to make the substitution $x=1/t$, so the limit becomes
$$
\lim_{t\to0^+}\frac{1+\sqrt[3]{t^3-1}}{t}=
\lim_{t\to0^+}\frac{1-\sqrt[3]{1-t^3}}{t}=
\lim_{t\to0^+}\frac{1-1+\frac{1}{3}t^3+o(t^3)}{t}
$$
