The solution in the book says $$ \frac{4}{5^{2/3}+5^{1/3}+5} $$ and the solution I calculated is $$ \frac{-25^{1/3}+5}{5} $$
Apparently these describe the same number.
However, I tried to show the equality and came nowhere.
Any idea on how to prove the equality?
Hint: A difference of cubes can be factored as $$x^3 - 1 = (x-1)(1+x+x^2).$$ Plugging in $x=5^{1/3}$, we have $$5-1=(5^{1/3}-1)(1+5^{1/3}+5^{2/3})=(1-5^{-1/3})(5^{1/3}+5^{2/3}+5).$$ Can you finish from here?