There are no "dependencies" per se for dynamic SQL because it's just text literals, so you have no defined dependencies to search on directly.

As far as I know the only way is to perform some sort of search on the text of the stored procedures, like....

DECLARE @Search varchar(255)

SET @Search='INPUT_SEARCH_HERE'

SELECT DISTINCT o.name AS Object_Name,o.type_desc

FROM sys.sql_modules m

INNER JOIN sys.objects o ON m.object_id=o.object_id

WHERE m.definition Like '%'+@Search+'%'

ORDER BY 2,1;