VMO 1975 Problem 2

Find all real x which satisfy ($x^3$ + $a^3$)/(x + a)$^3$ + ($x^3$ + $b^3$)/(x + b)$^3$ + ($x^3$ + $c^3$)/(x + c)$^3$ + 3(x - a)(x - b)(x - c)/( 2(x + a)(x + b)(x + c) ) = 3/2.