If $\sqrt[3]x-\sqrt[3]{x-14}=2$, find $x - 1/x$ 
$$ \sqrt[3]x-\sqrt[3]{x-14}=2$$
  Then find $x - \frac{1}{x} = ?$ 

I've tried to take third power of both sides but I couldn't find anything. 

Let $\sqrt[3]x=a,\sqrt[3]{x-14}=b$
$a-b=2, a^3-b^3=14$
Method$\#1:$
As $(a-b)^3=a^3-b^3-3ab(a-b)$
$2^3=14-3ab\cdot2\iff ab=1$
Method$\#2:$
$$a^3-(a-2)^3=14$$
