Here's another option that is inexpensive, easy and cures in about 5 minutes. Rough up the surface around the crack and wash clean with water. Then, open up the backside of crack with a Dremel tool. Not much. Just as YBK described. Blow dry. Put a piece of Gaffer tape on the visible side to hold the joint together, as tight as possible. (Do not duct tape, but get the stuff Film and TV gaffers use. Its properly adhesive, but tends not to pull off paint when removed).
Now, using the "original" super-glue, liberally lay down enough to fill the groove you've made on the back side. No worry if you over do it a bit. Then, quickly cover the super glue with baking soda. Acting quickly, blow off excess baking soda, then repeat with another, more copious dose of super glue and more baking soda. You need to have this compound laying over the crack by about double its original width. Blow off excess.
I have no clue to the magic of the chemistry behind this mix, but it is much stronger than the original plastic. It is very hard, but if done properly, the plastic will break in another spot before this bonding compound.
I've used this to fix many plastic parts over the years, including throttle housings. The trick is a rough, but clean surface before application. Absolutely, no petroleum or even oil from your fingers. Also, be careful to not let this stuff glue you fingers together. Surgical gloves are recommenced. This stuff can be sanded and Dremeled, but read warning below.
Warning: Do not breath the fumes that are created during the application process or during grinding or smoothing. It is much like sticking a piece of green Wasabe up you nose...I imagine.
