Yes, it will have to be removed if you plan on turning very much. I highly doubt you will even clear the cab, let alone a toolbox. I would bet there's a 98% chance you'll need a slider hitch. I extended the hitch on my
scamp, which is close to, if not 2' narrower than your trailer, and I still come quite close to hitting the cab with a 6.5' bed.
Easiest way is to find the spot in your bed right above your
axle. Now measure at least 3" ahead of that, at minimum. That's where your kingpin will be. Now measure the width of your trailer. You should have that distance (well, more) from the spot 3" ahead of your
axle to your cab. If not, you'll need a slider hitch.
I'm sure somebody on here will argue that, and here's my reply: I hope you have a low insurance deductible.
That one time, after a long day, a few flat
tires, a hard campsite, you being frustrated, and then smashing the crap out of your truck and trailer will make a slider hitch VERY cheap.