Find x in polynomial given value of inverse

Question

I'm studying for a test and this question has me really stumped:

$f(x) = 2x^3+5x+3$. Find x if $f^{-1}(x) = 1$

I don't know how I am supposed to figure out the inverse of this polynomial. I used this widget from Wolfram|Alpha to find the inverse, and it returned an enormous and confusing formula which doesn't seem humanly possible to calculate:

(not sure if the formula image generated by the widget will get deleted or not)

How would one even go about solving that type of problem?

Thanks

Answer 1

Hint: If $1 = f^{-1}(x)$, then $f(1) = f(f^{-1}(x)) = \dots$?