Do you know what "Cardano's method" is? If you do, it should be a matter of just doing the arthmetic!
If a and b are any real numbers, the and so that .
So if we let , , and , we have . Now, the question is "If we know m and n, can we find a and b?" (and so x).
From , we have . Putting that into , we have and, multiplying through by , which is equivalent to the quadratic equation for .
We can use the quadratic equation to solve that for : .
From , .
Once you have determined and , take the cube roots to find a and b and then find x= a- b. Of course, you will need to be careful about the three cube roots (two will be complex and one real).