If you make the change of variables y = X1/9 then the equation becomes
y3 - y = 60 or y3 - y - 60 = 0
Try some integer values for y to see if you can find a solution, say y = a. If so then
X = a9 is a solution to the original problem. Also, by the Factor Theorem, if y = a is a solution to y3 - y - 60 = 0 then (y-a) is a factor of y3 - y - 60 so by long division you should be able to find a quadratoc g(y) so that y3 - y - 60 = (y - a) g(y).