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Using a sample of (10087±44)×106 𝐽/𝜓 events, which is about 45 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 could be resolved by two overlapping resonant structures, 𝑋(1840) and 𝑋(1880). The new state 𝑋(1880) is observed with a statistical significance larger than 10𝜎. 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 𝑝¯ 𝑝 bound state.