Marked length spectra of Gromov hyperbolic space

Let $(X,d)$, $(Y,d^{\mathrm{\prime }})$ be two roughly geodesically complete Gromov hyperbolic spaces under comparable isometric actions of $\mathrm{\Gamma }$. Assume that the limit set $\mathrm{\Lambda }\mathrm{\Gamma }=\mathrm{\partial }X\mathrm{\partial }Y$. If spaces $X$ and $Y$ have the same asymptotic marked length spectrum, meaning that $$\underset{l_d([\gamma ])\to \mathrm{\infty }}{\lim }\frac{l_d(\gamma )}{l_{d^{\mathrm{\prime }}}(\gamma )}=1.$$ Then $(X,d)$ and $(Y,d^{\mathrm{\prime }})$ are $\mathrm{\Gamma }$-equivariantly roughly isometric.