INMO 1996 Problem 3

Solve the following system for real $a , b, c, d, e$ : $$\left\{ \begin{array}{ccc} 3a & = & ( b + c+ d)^3 3b & = & ( c + d +e ) ^3 3c & = & ( d + e +a )^3 3d & = & ( e + a +b )^3 3e &=& ( a + b +c)^3. \end{array}\right.$$