We consider a massive multiple-input multiple- output system with minimum-mean-squared-error processing on the uplink. A novel analytical framework is proposed to approximate the instantaneous signal-to-interference-plus-noise- ratio (SINR) of an arbitrary user terminal, as well as, the system sum spectral efficiency. Unlike previous studies, our methodology considers spatially correlated Ricean fading, with unequal Ricean K-factors, spatial correlation matrices and link gains across all terminals. Under this fully heterogeneous setting, we demonstrate that the SINR of a terminal can be tightly approximated by a linear combination of non-central chi-squared random variables, where the scaling depends on the individual link gains, K-factors, and eigenvalues of the terminal specific correlation matrices. Our approximations remain tight across the considered spatial correlation models, K-factor models, average uplink signal-to-noise-ratios and number of receive antennas. Leveraging the general form of the SINR and sum spectral efficiency, an analytical method to approximate their statistical moments is presented utilizing the moment generating function. The generality of the aforementioned analytical results is demonstrated via several special cases of practical relevance.