Along with what wader and Cannuck have said, the motion of the cast has
something to contribute as well.
If you're using a heavy lure (pickerel rig with weights for example) you
have no choice but to go with a smooth over the shoulder motion. However, if
you are using a lightweight lure such as a jig, spinner or such where the
weight is moderate to light and all of the weight is in one spot (jig head
versus lindy rig), then I have found that a very short arm motion with the
bulk of the rod motion coming from a snap motion of the wrist will give you
more distance and allow better control of where you place the lure as well.

I am not a fan of the braided lines, but I do not use mono either. Braided
lines tend to fray a lot in rough bottoms (logs, rocks) and mono is just too
fragile when you're after toothy critters. I use a superline like spiderwire
or gorilla line but never a braid. It's smaller diameter (4lb diameter for
12lb test as an example) does indeed give you better flex in the line for a
longer cast. And to avoid the twist that Wader refers to, use a swivel as
Canuck suggests. If it still develops, put a spinner or spoon on and cast
into river current. Let a lot of line out. If you're in a boat, you can just
use the swivel with no hook and let it out while the boat's moving. Let out
as much line as you can and simply retrieve it. the swivel allows the line
to straighten out again and remove the twist.

I've never fished with more than a 6.5 foot rod and am able to cast almost
as far as my friends with a ten foot noodle rod. It's all in the line
selection and the wrist motion.

Good luck!