How do I show that the curve x^3+y^3 = 3xy is symmetrical about the line y=x??

The curve is not one-to-one so I cant show that it is a self inverse. All I can think of is to show that the expression is the same when x and y are swapped. Is that enough??

Suppose that |x| and |y| (in the above expression) are both very large. Explain why x+y~k, where k is a constant?? Because the two expressions are the same when the variables are swapped??

Thanks