The completion of the hyperspace of finite subsets, endowed with the $\ell ^1$-metric

For a metric space $X$, let $\mathsf FX$ be the space of all non-empty finite subsets of $X$ endowed with the largest metric $d^1_{\mathsf FX}$ such that for every $n\in \mathbb N $ the map $X^n\to \mathsf FX$, $(x_1,\ldots ,x_n)\mapsto \{x_1,\ldots