I have repaired several broken rods by inserting a section inside the broken pieces, kinda like a spigot ferrule that has been glued. There are multiple gotcha's however.
1) First and foremost, review the break itself. If the blank is crushed, or has splinters running in both directions, don't even try!,
2) For an inserted plug, make sure the piece inserted is NOT more flexible than the rod itself. If it is, the rod will fail again in the same place. One fix for that is to insert a second piece inside the first plug to both stiffen it up and to make it stronger.
2) Next, make sure there is room to insert the plug! If in a tip section, it is not always possible to insert a plug in the broken area.
3) Then make sure the plug extends beyond the break by AT LEAST 1 1/2", in both directions. This will help prevent focusing the pressure right at the point of the break.
4) Make sure you use a quality epoxy! I use Pro Paste standard cure and have never had a problem. Do NOT use Gorilla Glue as it expands and forces its way through the cracks at the point of the break, and it is almost impossible to satisfactorily clean the glue off the blank.
5) Lastly, wrap over the repaired area with size "A" thread in a color that will disappear after applying thread-coat epoxy. This will make the repair virtually invisible.