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The homogeneous electron liquid is a cornerstone in quantum physics and chemistry. It is an archetypal system in the regime of slowly varying densities in which the exchange-correlation energy can be estimated with many methods. For high densities, the behavior of the ground-state energy is well-known for 1, 2, and 3 dimensions. Here, we extend this model to arbitrary integer dimensions and compute its correlation energy beyond the random phase approximation (RPA). We employ the approach developed by Singwi, Tosi, Land, and Sjölander (STLS), whose description of the electronic density response for 2D and 3D for metallic densities is known to be comparable to Quantum Monte-Carlo. For higher dimensions, we compare the results obtained for the correlation energy with the values previously obtained using RPA. We find that in agreement with what is known for 2 and 3 dimensions, the RPA tends to over-correlate the liquid also at higher dimensions. We furthermore provide new analytical formulae for the unconventional-dimensional case both for the real and imaginary parts of the Lindhard polarizability and for the local field correction of the STLS theory, and illustrate the importance of the plasmon contribution at those high dimensions.