Bicycle Mechanics - Regearing a MTB with road bike chainring & cassette?

I real like my cheap MTB (GT Aggressor). I only ride on roads, sidewalks, etc. What I don't like are the slow MTB speeds. I was thinking of getting a road bike because I like the speed, but I'm not sure they fit my application. A lot of the road I ride on are beat up pretty bad and I need to hop some curbs, etc on occasion. I don't want a hybred bike.

Would it be possible to have a road bike chain ring and cassette put on my MTB to incress the speeds? Even in my highest gear the road bikes effortlessly cruise right past me.

Are you spinning out in your highest gear?

First thing is get tires with street tread. That's a huge change.
I would change the cassette first, it's pretty cheap, and I don't think you need to change anything else to make it work. Perhaps a little adjustment of your derailleur adjustment screws, but I think it'll work immediately.
After trying the new cassette, see if you need to replace the chain rings. That's not cheap,but it is do-able.

I'll agree with the tire swap, that's simple enough. But changing the cassette only gets you an 11 if your smallest cost was a 12. Cheap, but maybe not enough of a difference. If you've got a 44T up front, you can go up to a 46 or 48. Of course, if your cadence isn't that high, then it doesn't matter. If you don't spin, you'll never go fast.

I happily run a 48/13 (96 gear-inch) top gear on my mountain bike, which would be about the same ratio as a 41/11 or a 44/12.

What size mtn cassette do you run?
My smallest cog was 12T so I replaced it with an 11T one. Like adding 3 teeth to your chainring.
If you have a triple, adding teeth to the mid ring is no problem, not a cage issue.
My chainstay dictates 38T ring mid max.
So I run 38 -11. Offroad bike.
If your cluster has a 12T..nowhere to go after 11 except after those chainrings.

14-28 HG cassette? Well there you go. No 12 cog.
You want a 12-28.
The small cog reach doesn't matter -like if you wanted to say run a 32T hill cog =you need a long cage derailer.
Get a 12-28. Try it first and if needed -get a 11T and lockring (you need the specific lockring).

Going to a 11 from 14 will slow you down..er....speed you up. Be quite a difference. ;)
11 from a 12 is just under 2 mph increase in speed, running a 38T ring, 80rpm.
One tooth =1.8 mph.

Like 35$ ? For the cluster.
I looked, your bike runs 38,48 I believe already.