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 $a + b + c + d = 100$.