It's probably best not to discuss it in terms of "leaving the Earth's atmosphere". The shuttle never really did, the atmosphere in some form goes out very far indeed.

However we *can* look at some times, velocities and burns.

For STS-135 these are the important times (given in minutes and seconds from liftoff)

- Solid rocket booster staging: 2:03
- Main engine cut-off: 8:23.8
- OMS-2 perigee-raising burn: 37:45

And the corresponding velocities

- Main engine cut-off: 25817 ft/s (28328 km/hr using the units you mentioned)
- OMS-2 delta-v: 96.8 ft/s (106 km/hr)

And the orbital parameters (units are nautical miles given as altitudes, all numbers are approximate)

- Main engine cutoff: Apogee 118 nm, Perigee 31 nm

- Post OMS-2: Apogee 124 nm, Perigee 84.9 nm

Sources: 

- [Space Shuttle Mission Summary][1]
- [STS-135 Space Reporter's Handbook][2]


  [1]: https://ntrs.nasa.gov/api/citations/20110001406/downloads/20110001406.pdf
  [2]: https://www.cbsnews.com/network/news/space/srh/SRH_135_best.pdf