This is a recurring problem. I do not have input on how to re-glue the Rods. And most Mooney models do not have access to the glue interface. If your Rods have snapped off the Bowden wire (Ø.056), here's how you at least access the glue interface.
1 Remove your Belly Panel.
2. Deploy your Flaps and Trim all the way up.
3. Under the aircraft, on the other end of the inner Bowden wire, mark the wire on either side of the clamping mechanism. You may have to perform some later adjustments to calibrate your Flap/Trim Indicators, but this will allow you to align later and remain close.
4. Loosen the clamping mechanisms and push the wire into the Boden Sleeve. Don't worry if it disappears into the sleeve. You can push it down from the other end.
5. Go back to the cockpit. The Bowden cable ends will now be pushed up further ... at least enough to grab with needle nose pliers.
6. I would suggest pulling the wires largely (not completely) out and lubing them with Aeroshell 22 or the like. The trim cable is long and it's not a sealed cable. It can get quite stiff.
7. Reattach your Acrylic Rods using other members' input. I believe the factory used Permabond 910 Clear Methyl Cyanoacrylate Adhesive (used to be made by a company called Easton). METHYL Cyanoacrylate adhesive is a little more robust than plain Cyanoacrylate adhesive (super glue). Other members used epoxy.
Good luck, Ken