Let

t = x^(1/3)

and replace into the equation 

you will get

3t^2 - 13t + 4 = 0

Solve the above quadratic equation and you will get the following solutions

Click here to see the step by step solution for t

t1 = 4

t2 = 1/3

Now go back to finding "x".

For t = 4 we have

x^(1/3) = 4

x = 4^3

x = 64

For t = 1/3 we have

x^(1/3) = 1/3

x = (1/3)^3

x = 1/27

The solutions are 64 and 1/27/