I'm struggling with this one:

How many incongruent solutions are there to the congruence $\displaystyle x^5 + x - 6 = 0(mod 144)$?

I know I have to use Hensel's Lemma here. But the examples I've seen the mod is easily factored (e.g. $\displaystyle 27 = 3^3$, or $\displaystyle 25 = 5^2$) so those examples aren't exactly the same as what is presented here I'm guessing since 144 is $\displaystyle 2^4 * 3^2$