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-- Select the fat line, and do Path menu > Stroke to Path (Or if you draw a long, skinny rectangle, instead of a stroked path, skip this step.)
-- Position the line (or rectangle) over the text
-- Select both line and text
-- Path menu > Difference
Edit
Hhm, just noticed a drop shadow under the text in your example. So this would not affect that drop shadow. Also, if the drop shadow is grouped with the text, you'll need to either enter the group, or ungroup first.