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We present a 3D mapping of the Wolf-Rayet (WR) nebula M 1-67 around WR 124. We obtained high-resolution San Pedro Martir (SPM) Manchester Echelle Spectrograph (MES) observations along 17 long-slit positions covering all morphological features in M 1-67. We are able to unveil the true morphology of M 1-67 and its kinematics by interpreting the SPM MES observations by means of the 3D modelling tool for Astrophysics SHAPE. Our SHAPE model that best reproduces the SPM MES data includes three concentric bipolar structures composed by a hollow ellipsoidal structure and a torus. In addition, the model requires the presence of expanding jets and broken blisters in order to reproduce specific spectral features. Our results are consistent with the idea that M 1-67 and its progenitor star WR 124 have formed through a common envelope scenario that occurred 11.8^{+4.6}_{-0.8} kyr ago. Our bipolar model strongly questions previous suggestions of the presence of a bow shock structure surrounding M 1-67. We interpret that the bright structures detected in the spectra extracted from the central regions are produced by wind compression at the receding region of the innermost structure in M 1-67. Furthermore, WR 124 is moving through a low-density region above the Galactic plane that has negligibly affected the formation history of M 1-67.