We have developed a novel technique to extract isospin-breaking effects in particle decays that do conserve them. This technique is based in taking experimental data used in Dalitz plots and map it into unit disks, so as to compare two disks from related processes directly. In this case we apply it to $\eta'\to\eta\pi^+\pi^-$ and $\eta'\to\eta\pi^0\pi^0$ decays. We have constructed such Dalitz disks using BES-III data and computed the theoretical decay width to fit the isospin-breaking parameter $Q^2=(\hat{m}^2-m_s^2)/(m_u^2-m_d^2)$, using the same binning for both disks. The theoretical expressions were computed using Large $N_C$-$\chi$PT and the disks from pseudodata generated using BES-III parameters for both decay channels.