$$\sum_{n=1}^\infty \frac{(n!)(iz+1)^n} {n^3+ \sqrt[3] {n}} $$

which test should be used in this case?

I tried the ratio test, but the terms did not cancel out (some did):

$\lim_{n\to \infty} \frac{(n+1)!(iz+1)^{n+1}} {(n+1)^3 + \sqrt[3] {n+1}} \frac {n^3+ \sqrt[3] {n}} {(n!)(iz+1)^n} $

$\lim_{n\to \infty} \frac{(n+1)(iz+1)} {(n+1)^3 + \sqrt[3] {n+1}} \frac {n^3+ \sqrt[3] {n}} {1} $

I am kind of stuck at this point. Any help to pass this point is appreciated.