Can the sum of two cube roots of positive non-perfect cubes be an integer?

Give reasons for your answer.

Since nothing was said about a and b being integers, take a=(x+y)^3 and b=(x-y)^3 where x is an integer and y is an irrational, say x=2 and y=2^1/2.  Then the sum of the cube roots of a and b is the integer 4.

Posted by xdog on 2015-08-14 20:12:21