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Results from a partial-wave analysis of the decay J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}${\mathit{K}}_{\mathit{S}}^{0}$${\mathit{K}}^{\ifmmode\pm\else\textpm\fi{}}$${\mathrm{\ensuremath{\pi}}}^{\ensuremath{\mp}}$ in the ${\mathit{K}}_{\mathit{S}}^{0}$${\mathit{K}}^{\ifmmode\pm\else\textpm\fi{}}$${\mathrm{\ensuremath{\pi}}}^{\ensuremath{\mp}}$ invariant-mass range 1.35--1.6 GeV/${\mathit{c}}^{2}$ are presented. Within the isobar model, the data in this mass range are best described by a mixture of ${0}^{\mathrm{\ensuremath{-}}+}$ and ${1}^{++}$ amplitudes, corresponding to the ${\mathit{K}}^{\mathrm{*}}$K\ifmmode\bar\else\textasciimacron\fi{}+c.c (P wave), ${\mathit{K}}^{\mathrm{*}}$K\ifmmode\bar\else\textasciimacron\fi{}+c.c (S wave), and ${\mathit{a}}_{0}$(980) \ensuremath{\pi} (S wave) channels. These results show that \ensuremath{\eta}(1430) is not a ${\mathit{J}}^{\mathit{P}\mathit{C}}$=${0}^{\mathrm{\ensuremath{-}}+}$ ${\mathit{a}}_{0}$(980)\ensuremath{\pi} resonance, but a mixture of overlapping states.