how to remove empty strings from list, then remove duplicate values from a list

Lets say I have a list of some column values coming from a table, how do I remove empty strings and duplicate values. Please see the following code:

List<string> dtList = dtReportsList.AsEnumerable().Select(dr => dr.Field<string>("column1")).ToList();

This is what I have coded just now but but Amiram's code is way more elegant, so I will choose that answer here is how I did it:

DataTable dtReportsList = someclass.GetReportsList();

        if (dtReportsList.Rows.Count > 0)
       { 
           List<string> dtList = dtReportsList.AsEnumerable().Select(dr => dr.Field<string>("column1")).ToList();
           dtList.RemoveAll(x=>x == "");
           dtList = dtList.Distinct().ToList();         

           rcboModule.DataSource = dtList;
           rcboModule.DataBind();               
           rcboModule.Items.Insert(0, new RadComboBoxItem("All", "All"));
       }