  Using the pull-back of the perturbed type IIA metric corresponding to the
perturbation of arXiv:hep-th/1306.4339's M-theory uplift of
arXiv:hep-th/0902.1540's UV-complete top-down type IIB holographic dual of
large-$N$ thermal QCD, at finite coupling, we obtain the interaction Lagrangian
corresponding to exotic scalar glueball($G_E$)-$\rho/\pi$-meson interaction,
linear in the exotic scalar glueball and up to quartic order in the $\pi$
mesons. In the Lagrangian, the coupling constants are determined as (radial
integrals of) arXiv:hep-th/1306.4339's M-theory uplift's metric components and
six radial functions appearing in the M-theory metric perturbations. Assuming
$M_G>2M_\rho$, we then compute $\rho\rightarrow2\pi, G_E\rightarrow2\pi, 2\rho,
\rho+2\pi$ decay widths as well as the direct and indirect (mediated via $\rho$
mesons) $G_E\rightarrow4\pi$ decays. For numerics, we choose $f0[1710]$ and
compare with previous calculations. We emphasize that our results can be made
to match PDG data (and improvements thereof) exactly by appropriate tuning of
some constants of integration appearing in the solution of the M-theory metric
perturbations and the $\rho$ and $\pi$ meson radial profile functions - a
flexibility that our calculations permits.
