Let $\mathcal A$ be a unital complex algebra, let $\varphi: \mathcal A \to \mathbb C$ be a unital linear functional, and let $(\mathcal A,\varphi)$ be the resulting scalar-valued noncommutative probability space. Let $\mathcal B,\mathcal C \subset \mathcal A$ be unital subalgebras, with the same unit as $\mathcal A$, that are free with respect to $\varphi$. Let $a \in \mathcal B$ and $b \in \mathcal C$. For every $n \in \mathbb N$, let $\kappa_n: \mathcal A^n \to \mathbb C$ denote the $n$-th scalar-valued free cumulant functional associated to $\varphi$. Then

\begin{align*} \kappa_n(a+b,\dots,a+b)=\kappa_n(a,\dots,a)+\kappa_n(b,\dots,b). \end{align*}