The anisotropic galaxy clustering of large scale structure observed by the Baryon Oscillation Spectroscopic Survey Data Release 11 is analyzed to probe the sum of neutrino mass in the small $m_ u < 1eV$ limit in which the early broadband shape determined before the last scattering surface is immune from the variation of $m_ u$. The signature of $m_ u$ is imprinted on the altered shape of the power spectrum at later epoch, which provides an opportunity to access the non--trivial $m_ u$ through the measured anisotropic correlation function in redshift space (hereafter RSD instead of Redshift Space Distortion). The non--linear RSD corrections with massive neutrinos in the quasi linear regime are approximately estimated using one-loop order terms computed by tomographic linear solutions. We suggest a new approach to probe $m_ u$ simultaneously with all other distance measures and coherent growth functions, exploiting this deformation of the early broadband shape of the spectrum at later epoch. If the origin of cosmic acceleration is unknown, $m_ u$ is poorly determined after marginalising over all other observables. However, we find that the measured distances and coherent growth functions are minimally affected by the presence of mild neutrino mass. Although the standard model of cosmic acceleration is assumed to be the cosmological constant, the constraint on $m_ u$ is little improved. Interestingly, the measured CMB distance to the last scattering surface sharply slices the degeneracy between the matter content and $m_ u$, and the hidden $m_ u$ is excavated to be $m_ u=0.19^{+0.28}_{-0.17} eV$ which is different from massless neutrino more than 68% confidence.
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