Find the maximal value of where , , , are nonnegative real numbers which satisfy .
Find the maximal value of
\[S = \sqrt[3]{\frac{a}{b+7}} + \sqrt[3]{\frac{b}{c+7}} + \sqrt[3]{\frac{c}{d+7}} + \sqrt[3]{\frac{d}{a+7}},\]where $a$, $b$, $c$, $d$ are nonnegative real numbers which satisfy $a+b+c+d = 100$.
Školjka ![S = \sqrt[3]{\frac{a}{b+7}} + \sqrt[3]{\frac{b}{c+7}} + \sqrt[3]{\frac{c}{d+7}} + \sqrt[3]{\frac{d}{a+7}},](/media/m/f/6/5/f65475dcb0df99b384f915c2001a7ee1.png)
where 
, 
, 
, 
are nonnegative real numbers which satisfy 
.