I'm trying to use the Zoom G3X effects in conjunction with the 11R. (It has a few sounds that the 11R doesn't have that I'm interested in.) To do this, I'm trying to run it through the virtual FX pedal in the unit. However, it doesn't work. There's no signal coming through the G3X, as if it isn't even connected. The appropriate levels in the 11R for the loop seem to be set correctly.

If I move the Zoom G3X outside of the loop and place it before the amp, the G3X works, but this is not an acceptable solution because the effects don't sound right using this method.

I have the sense though that this is not a problem specific to the G3X, but that I must not be aware of a certain setting I must change on the 11R in order to get the signal flowing through the G3X. (I have never tried to use the FX loop to bring in an external effect controller.)

Any advice regarding what I might try to do?

Do you have the FX loop turned ON on the 11R? And the mix control set to more than 0%? The mix setting is on the edit page of the FX loop, where you also find a bypass button. This corresponds with the FX Loop button on the front panel of the 11R. I would check these details first.
If that doesn't help, double-check your connections: fx send to the input of the Zoom, output of the Zoom to fx return. Check the cables. Check the input and output levels of the Zoom. Make sure you set the fx loop to the right level (it is switchable on the back panel to adjust to both rack effect units and foot pedals).

I haven't tried the 11R FX loop, but a week ago or so I tried my amp's FX loop with my Zoom G7.1ut. The 11R was plugged into the amp's main input and the EQ adjusted accordingly. It sounded fantastic. Then I put the G7.1 in the loop - amp & cab turned off, of course - and... well, let's just say I can't recall ever having heard a worse guitar sound.

On its own the Zoom sounds... well, not great, but OK. The clean sounds are nice and I do like the effects. On its own my Seymour Duncan 84-40 sounds OK. On its own the 11R sounds really good. Put the 11R into the amp and something magical happens... it becomes awesome. Add the Zoom through the effects loop... and the whole thing turns to poop. I really don't know why. Now this was just an experiment and I don't need that kind of setup but it was, nonetheless, rather disappointing. The G7.1 went back into its case, likely for a very long time. It's a shame... as I mentioned, the effects are very good in the Zoom.