thanks for the help, i have tried this approach, and the come to the point where I have the following expressions for k,m,l:
k^3 = (1/4)b^3 + (1/2)c^3
m^3 = (1/16)a^3 - (1/4)c^3
l^3 = (1/32)a^3 - (1/16)b^3
and i plug these into the original equation and the a terms do not cancel out...