Brake issue - Car and car and steering wheel move towards right

Recently I am having some problem with my 2001 Toyota Camry SE (110000 miles), while driving more than 50 miles speed. If I apply break the car and steering wheel try to move towards right. However car doesn’t shake and seems like it taking slight longer time to apply the brake. I took it to a local repair store. They checked and clean the brake pad but problem still exists. Wondering, anyone had similar problem before?

have you had a brake job done before/recently? How long ago?
Some issues that may cause this:
a sticking brake caliper, a stuck brake pad (or two), or poor quality brake pads (from a recent brake job.

What type repair store did you take this too? Most quickie chains would not have the expertise to figure out the problem. They would only throw new pads on and send you on your way. How long since last brake job? were calipers or rotors replaced? Did you take it to the place you had the brakes done at last? Or to a different shop?

Just pretend that your car was built in the 1920s and then what you describe would be more or less as normal. Alfred P. Sloan in his book about his time with General Motors said that a typical 1920s car would veer to one side when the brakes were applied.

You may have unequal front braking action, likely traceable to a stuck front caliper slide due to corrosion. This should be a simple repair if my guess is correct. Cleaning the brake pads may not be appropriate as brake pads are self cleaning to a great extent.