Let \( n \) be a positive integer. Determine all continuous functions \(f: [0, 1] \to \mathbb{R}\) such that
\[
f(x_1) + \dots + f(x_n) =1
\]
for all \( x_1, \dots, x_n \in [0, 1] \) satisfying \( x_1 + \dots + x_n = 1\).