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We report muon spin rotation and magnetic susceptibility experiments on in-plane stress effects on the static spin-stripe order and superconductivity in the cuprate system La2−xBaxCuO4 with x=0.115. An extremely low uniaxial stress of ∼0.1 GPa induces a substantial decrease in the magnetic volume fraction and a dramatic rise in the onset of 3D superconductivity, from ∼10 to 32 K; however, the onset of at-least-2D superconductivity is much less sensitive to stress. These results show not only that large-volume-fraction spin-stripe order is anticorrelated with 3D superconducting coherence but also that these states are energetically very finely balanced. Moreover, the onset temperatures of 3D superconductivity and spin-stripe order are very similar in the large stress regime. These results strongly suggest a similar pairing mechanism for spin-stripe order and the spatially modulated 2D and uniform 3D superconducting orders, imposing an important constraint on theoretical models.