Nested IF functions in excel with blank cells

Checked through a few other questions and can't see the same issue. Perhaps I am approaching this from the wrong angle. Any help or advice appreciated.

I have a worksheet which contains contact details, and a second worksheet which reformats these to be imported into a 3rd party system. I am using a column containing 'X' to pick out those to be migrated. My issue comes when people have provided a home number and no mobile number or vice versa, for the import to work all numbers must be in the same column, so I need to nest a second IF function which asks subsequently, if the cell is blank, go to the next cell.

Essentially merging these two statements (below)? - But not sure how!

=IF('Master contacts list'!M10="X",'Master contacts list'!H10, IF('Master contacts list'!H10="",'Master contacts list'!J10))

Perhaps I should use multiple logical statements instead, but can't get my head around this either...