  We analyse the anisotropic clustering of the Baryon Oscillation Spectroscopic
Survey (BOSS) CMASS Data Release 11 (DR11) sample, which consists of $690\,827$
galaxies in the redshift range $0.43 < z < 0.7$ and has a sky coverage of
$8\,498\,\text{deg}^2$. We perform our analysis in Fourier space using a power
spectrum estimator suggested by Yamamoto et al. (2006). We measure the
multipole power spectra in a self-consistent manner for the first time in the
sense that we provide a proper way to treat the survey window function and the
integral constraint, without the commonly used assumption of an isotropic power
spectrum and without the need to split the survey into sub-regions. The main
cosmological signals exploited in our analysis are the Baryon Acoustic
Oscillations and the signal of redshift space distortions, both of which are
distorted by the Alcock-Paczynski effect. Together, these signals allow us to
constrain the distance ratio $D_V(z_{\rm eff})/r_s(z_d) = 13.89\pm 0.18$, the
Alcock-Paczynski parameter $F_{\rm AP}(z_{\rm eff}) = 0.679\pm0.031$ and the
growth rate of structure $f(z_{\rm eff})\sigma_8(z_{\rm eff}) = 0.419\pm0.044$
at the effective redshift $z_{\rm eff}=0.57$. We did not find significant
systematic uncertainties for $D_V/r_s$ or $F_{\rm AP}$ but include a systematic
error for $f\sigma_8$ of $3.1\%$. Combining our dataset with Planck to test
General Relativity (GR) through the simple $\gamma$-parameterisation, reveals a
$\sim 2\sigma$ tension between the data and the prediction by GR. The tension
between our result and GR can be traced back to a tension in the clustering
amplitude $\sigma_8$ between CMASS and Planck.
