What I would do in this case is just get rid of that "1/3" by using some notations:
a^(1/3) = x
b^(1/3) = y
You initially get that x^2 - y^2 = 12, which is the equivalent of (x - y)(x + y) = 12.
1. gives us x - y = 2. Since (x - y)(x + y) = 12, this means that x + y = 12/2 = 6. If you revert back to the notation, then you get that a^(1/3) + b^(1/3) = 6, which is exactly what you are looking for. So 1 is sufficient.
2. states that a = 4, which means that b^(2/3) = 12 - 4^(2/3). Now, the problem with finding out b^(1/3) is that either b^(1/3) or -b^(1/3), when raised to the second power, equal 12 - 4^(2/3). Since you do not have additional info, you can't pick between the two, meaning that you can't find out a^(1/3)+b^(1/3). So 2 is insufficient.
My guess is indeed the OA.
