Find out maximum as well as minimum

$\large{ p\leq 4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4)\leq q }$

Let the real numbers $a,b,c,d$ satisfy the relations $a+b+c+d=6$ and $a^2+b^2+c^2+d^2=12$ . If above inequality is satisfied for some positive integers $p$ and $q$ . Find the value of $p+q$