Interesting project, if you can post a picture of the dresser, with dimensions, you may get some additional comments. Also, the slides that are typically used for drawers are not suitable for file cabinet use, and after seeing the recent articles about furniture falling over, you would need to be very careful that with a fully loaded file drawer, the dresser would remain upright as the drawer was opened.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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