Problem of the Day #30 (Challenge)

POTD Challenge December 19, 2023
Author: munch

If a,b,c,d are non-negative real numbers such that\frac{(a+b+c+d)^3}{3} + (a+b+c+d)(a^2+b^2+c^2+d^2) = \frac{4(a^3+b^3+c^3+d^3)}{3}, find the sum of all values of ab+ac+ad+bc+bd+cd.