  Modified gravity models with scale-dependent linear growth typically exhibit
an enhancement in the power spectrum beyond a certain scale. The conventional
methods for extracting cosmological information usually involve inferring
modified gravity effects via Redshift Space Distortions (RSD), particularly
through the time evolution of $f\sigma_8$. However, classical galaxy RSD
clustering analyses encounter difficulties in accurately capturing the
spectrum's enhanced power, which is better obtained from the broad-band power
spectrum. In this sense, full-shape analyses aim to consider survey data using
comprehensive and precise models of the whole power spectrum. Yet, a major
challenge in this approach is the slow computation of non-linear loop integrals
for scale-dependent modified gravity, precluding the estimation of cosmological
parameters using Markov Chain Monte Carlo methods. Based on recent studies, in
this work we develop a perturbation theory tailored for Modified Gravity, or
analogous scenarios introducing additional scales, such as in the presence of
massive neutrinos. Our approach only needs the calculation of the
scale-dependent growth rate $f(k,t)$ and the limit of the perturbative kernels
at large scales. We called this approximate technique as fk-Perturbation Theory
and implemented it into the code fkpt, capable of computing the redshift space
galaxy power spectrum in a fraction of a second. We validate our modeling and
code with the $f(R)$ theory MG-GLAM and General Relativity NSeries sets of
simulations. The code is available at https://github.com/alejandroaviles/fkpt
