a^3 + b^3 + c^3 = d^3

I have so far found the following, which of course does not generate all possible a, b, c, and d:

a = 9x^3 - 1
b = 9x^4 - 3x
c = 1
d = 9x^4

Also, I think it is possible to choose integers p and q:

d = p + q
c = p
a^3 + b^3 = q^3 + 3pq( p + q )

and now also:

( a + b )( a^2 + b^2 - ab) = ( d - c )( d^2 + c^2 + cd )

Is this any progress towards solving the problem?

a = x
b = 3x^2 + 2x + 1
c = 3x^3 + 3x^2 + 2x
d = 3x^3 + 3x^2 + 2x + 1