GAIC Math 2024 Problem 56

Given $(n + 1)^{a+1} - n^{a+1} < n a^(a + 1) < n a^{n+1} - (n - 1)^{a+1} (-1 < a < 0) \textcircled{1}$. Let$x=\sum\limits_{k=4}^{106}\frac{1}{\sqrt[3]{k}}$, then the integer part of x is _____.