Question 28
Find the minimum positive integer $n$ such that
$$
\sqrt{\frac{n-2011}{2012}} - \sqrt{\frac{n-2012}{2011}} \lt \sqrt[3]{\frac{n-2013}{2011}} - \sqrt[3]{\frac{n-2011}{2013}}
$$
$$
\sqrt{\frac{n-2011}{2012}} - \sqrt{\frac{n-2012}{2011}} \lt \sqrt[3]{\frac{n-2013}{2011}} - \sqrt[3]{\frac{n-2011}{2013}}
$$