Shinner, I'm afraid you can't build 3D references in the manner.
For an INDIRECT construct you would need to detail all sheets individually within the start:end sheet references rather than just the start & end sheet references themselves.
You might want to consider use of VBA - ie a Volatile UDF.
Function Sum3D(strWS1 As String, strWS2 As String, rngSum As Range)
Application.Volatile
Sum3D = Evaluate("SUM('" & strWS1 & ":" & strWS2 & "'!" & rngSum.Address & ")")
End Function
the above stored in a standard module in VBE would be called from a cell along the lines of:
=Sum3D(VLOOKUP("country1",A:C,3,FALSE),VLOOKUP("country5",A:C,3,FALSE),C1)
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