  Thin films of the optimally electron-doped $T'$-phase superconductor
La$_{1.89}$Ce$_{0.11}$CuO$_{4\pm \d}$ are investigated by dilute Co doping,
formed as La$_{1.89}$Ce$_{0.11}$(Cu$_{1-x}$Co$_{x}$)O$_{4\pm\d}$ (LCCCO) with
$x$ = 0.01 -- 0.05. The following results are obtained for the first time: for
the whole dilute Co doping range, LCCCO thin films show long-range
ferromagnetic ordering at the temperature range from 5 K to 300 K, which is
likely due to the RKKY interaction; in the very dilute Co doping, $x$ = 0.01
and 0.02, the superconductivity is maitained, the system shows the coexistence
of superconductivity and ferromagnetism in the CuO$_{2}$ plane. This may be
based on the nature of the charge carriers in electron-doped high-$T_{c}$
cuprate superconductors.
