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 $D_V(z_{rm eff})/r_s(z_d) = 13.89pm 0.18$, the Alcock-Paczynski parameter $F_{rm AP}(z_{rm eff}) = 0.679pm0.031$ and the growth rate of structure $f(z_{rm eff})sigma_8(z_{rm eff}) = 0.419pm0.044$ 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 $fsigma_8$ of $3.1%$. Combining our dataset with Planck to test General Relativity (GR) through the simple $gamma$-parameterisation, reveals a $sim 2sigma$ 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.
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