Well if you have a cube thats 5 by 5 by 5, the volume is 125 cubic units. The cube root of 125 will tell you the length of a side, not the surface area or area of one face.
So no, the cubic root of volume does not give you area. On top of that, for any shape other than a cube, the area of each face is different. So you have to know what the shape is to know how to find the surface area or the area of one face.