Sum of Max, Min

For the radical equation, equality can only be achieved when $x=-4$ . For the quadratic function, it can be written as $f(x) = 3(x-1)^2 - 4$ which has a global minimum value of $-4$ . The maximum value is calculated per $f(-4) = 3(-5)^2 - 4 = 71$ . Thus, $f_{MAX} + f_{MIN} = 71 - 4 = \boxed{67}.$