Question posed by my peruvian teacher of calculus

Calculus Level 4

L=limx1x3x1xL= \large \lim_{x \to 1} \frac { \sqrt[3]{x} - \sqrt{x} }{1 - x}

If LL can be expressed as ab \frac a b , where a,ba,b are coprime positive integers, what is the value of a+ba+b?

Remark: try not to use L'Hôpital's rule.

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