IOM 2021 Problem 4

Six real numbers $x_1<x_2<x_3<x_4<x_5<x_6$ are given. For each triplet of distinct numbers of those six Vitya calculated their sum. It turned out that the $20$ sums are pairwise distinct; denote those sums by $$s_1<s_2<s_3<\cdots<s_{19}<s_{20}.$$ It is known that $x_2+x_3+x_4=s_{11}$ , $x_2+x_3+x_6=s_{15}$ and $x_1+x_2+x_6=s_{m}$ . Find all possible values of $m$ .