.mlx files can have function definitions in them in recent MATLAB versions, provided that the function has a matching "end" statement.
It is not possible to "bundle" a .m file with a .mlx file, except by creating an "app"; https://www.mathworks.com/help/matlab/packaging-guis-as-apps.html?s_tid=CRUX_lftnav which creates a .mlappinstall file