The sum of a number, its cube root and square is 759. What is the number?

So we have

 N^2 + N + N^(1/3) = 759

Let's assume that the number we're looking for is an integer.

And let's first take the sq root of 759 = about 27.55

Then 759  is a little larger than 27^2

Let's test 27

27^2 + 27  + 27^(1/2) =

729 + 27 + 3  = 

759

So.....27 is the integer we were looking for....