FULL DISCLOSURE: I work for an ophthalmology practice that performs LASIK. However, I wouldn’t bullshit you. 
enipla, what you have right now is two separate problems.
First, since you need glasses or contacts for distance vision, you’re myopic (nearsighted). This is a mechanical defect in the eye: basically, the geometry of a myopic eye is such that light (and images) coming through your cornea converge in front of your retina instead of exactly on it. LASIK does a great job of correcting myopia; it reshapes your cornea to compensate for the geometric problem, and most nearsighted people can see great after LASIK.
Second, you’re starting to need reading glasses for close work. This is presbyopia, a result of the natural aging of your eye. It happens to everyone, and it usually becomes noticeable between 45 and 55. What’s happening is that your eye’s natural lens - suspended directly behind your iris in a web of muscle and connective tissue - is growing thicker each year, much like a tree putting on rings. At the same time, the muscles holding the lens, whose job it is to flex and move that lens and allow you to focus, are losing their tone. Eventually, the lens becomes too thick for the muscles to move around, and you lose the ability to focus on near objects. (Incidentally, as the lens grows thicker, it grows more opaque as well. When it gets too opaque to see through, you have cataracts.)
There are LASIK solutions for presbyopia, but they involve trade-offs. The most popular solution is called monovision or blended vision, and you’ve already said you don’t want it. It’s the process where one eye is optimized for close work and the other eye is set up for distance work. It sounds weird (hell, it sounds dizzying), but in a high percentage of people it works well. The brain learns, over the course of a few weeks, which eye is for which, and it sort of shuts out the visual “noise.” Depth perception is never the same as it was before, but blended vision does allow most people to get my without reading glasses or bifocals. Any decent LASIK clinic will allow you to “try on” blended vision - they’ll give you a pair of glasses or contacts to simulate what the procedure will do for you, and you can see if you like it.
I hope that helps a little. I had LASIK myself and it’s one of the greatest feelings of my life, but then again I’m 34 and haven’t had to worry about presbyopia yet. I don’t know what I would do in your case. If you decide you want to at least look into it (pretty much every LASIK clinic offers free initial screenings and consultations), let me know and I’ll give you more specifics on how to pick out a good clinic - there are tons of them out there, in a broad range of prices, and they are not created equal.