I wouldnt recommend putting the ferrule inside the rod, but use it as a sleeve over the two broken sections....
Find an old tip section from a rod with a
lower modulus than the tip your fixing (in a nutshell a softer rod) You might be able to get a scrap one from you local friendly tackle dealer.
Cut off a 30mm (ish) section off it at a point where the internal diameter is just large enough so it will just push over the end of the rod where it broke to make a spogot. it wants to be a good tight fit if poss.
Then push the broken off tip into the other end of the spigot so that the junction between the two broken sections is in the middle of the spigot. You might need to take a bit of wet and dry to the parts of the joint to get a nice sound fit - but this is fine as long as your only removing varnish/laquer, and not disturbung the carbon of the blank.
When putting it all together, then dab a TINY amount of araldite inside and at each end of the spigot to hold it al in place.
(Before putting it all together you can slim the spigot down to the carbon with wet and dry to give it a slimmer profile if your brave.
Now, tightly whip the whole joint, and continue about a 1/4" of wraps before and after the spigot, then varnish to seal.
You would hardly even know its there unless you studied the blank closely.
If your even luckier, if its near a ring, you can sometimes move the ring to sit over the join, in wich case the whippings would look like the ones for the ring.
Graeme