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Using a sample of (10087±44)×106 J/ψ events, which is about fifty times larger than that was previously analyzed, a further investigation on the J/ψ→γ3(π+π−) decay is performed. A significant distortion at 1.84 GeV/c2 in the line-shape of the 3(π+π−) invariant mass spectrum is observed for the first time, which is analogous to the behavior of X(1835) and could be resolved by two overlapping resonant structures, X(1840) and X(1880). The new state X(1880) is observed with a statistical significance of 14.7σ. The mass and width of X(1880) are determined to be 1882.1±1.7±0.7 MeV/c2 and 30.7±5.5±2.4 MeV, respectively, which indicates the existence of a pp¯ bound state.