#[05AB1E](https://github.com/Adriandmen/05AB1E/wiki/Commands), <s>8 (or 10?)</s> 11 (or 13?) [bytes](https://github.com/Adriandmen/05AB1E/wiki/Codepage)

    Ÿʒ₄n+¦S3ôOË

[Try it online](https://tio.run/##MzBNTDJM/f//6I5Tkx41teRpH1oWbHx4i//h7v//DYwtLE0NuECUgQEA) or [verify some more test cases](https://tio.run/##MzBNTDJM/W/q5un5/@iOU5MeNbXkaR9aFmx8eIv/4e7/tTr/DYwtLE0NuECUAZAyMDSAUIZgygjCMwLxjIzAPCAFkTMwgGkwBAA).

NOTE: In 05AB1E strings and integers are interchangeable, so the output numbers doesn't contain leading zeroes. This could however be fixed with 1 additional byte (**12 bytes**):

    Ÿ₄n+€¦ʒS3ôOË

[Try it online](https://tio.run/##MzBNTDJM/f//6I5HTS152o@a1hxadmpSsPHhLf6Hu///NzC2sDQ14AJRBgYA) or [verify some more test cases](https://tio.run/##MzBNTDJM/W/q5un5/@iOR00tedqPmtYcWnZqUrDx4S3@h7v/1@r8NzC2sDQ14AJRBkDKwNAAQhmCKSMIzwjEMzIC84AURM7AAKbBEAA).

+3 bytes to bug-fix numbers with a length of 3 or less (range `[000000, 000999]`).

**Explanation:**

<!-- language-all: lang-python -->

    Ÿ          # Create an inclusive (on both sides) range from the two inputs
               #  i.e. 038920 and 038910 → 
               #   [38910,38911,38912,38913,38914,38915,38916,38917,38918,38919,38920]
     ʒ         # Filter this list by:
      ₄n+      #  Add 1,000,000 to the number
         |     #  And remove the leading 1
               #   i.e. 38910 → 1038910 → '038910'
      S        #  Transform it to a list of digits
               #   i.e. '038910' → ['0','3','8','9','1','0']
       3ô      #  Split it into chunks of length 3
               #   i.e. ['0','3','8','9','1','0'] → [['0','3','8'],['9','1','0']]
         O     #  Sum the digits in both parts
               #   i.e. [['0','3','8'],['9','1','0']] → [11,10]
          Ë    #  Check if they are equal (if they are, they remain in the filtered list)
               #   i.e. [11,10] → 0

----------

EDIT: Seems I (and most other answers) slightly misread the challenge and the amount of numbers is being asked instead of the numbers themselves within the range. In that case a trailing `}g` can be added (close the filter; and get the amount of numbers left in the filtered list), so it's **<s>10</s> 13 [bytes](https://github.com/Adriandmen/05AB1E/wiki/Codepage)** instead:

    Ÿʒ₄n+¦S3ôOË}g

[Try it online](https://tio.run/##MzBNTDJM/f//6I5Tkx41teRpH1oWbHx4i//h7tr0//8NjC0sTQ24QJSBAQA) or [verify some more test cases](https://tio.run/##MzBNTDJM/W/q5un5/@iOU5MeNbXkaR9aFmx8eIv/4e7a9P86/w2MLSxNDbhAlAGQMjA0gFCGYMoIwjMC8YyMwDwgBZEzMIBpMAQA).