Cut And Paste Only Visible Cells In Filtered Area

I have a data of a large no. of rows with 5 columns. The last 2 columns are district and state. As it is an imported data, in some rows the data has shifted a column, i.e. the name of state is being shown in district column and name of district is being shown in the column to its left. I tried filtering the data such that it shows only those rows where names of the states are coming under district columns and then selecting the whole thing, cutting it and pasting it to the rightmost column. But even the correct district entries got pasted under state column. Undo, the further damage was controlled, but the original problem remains. Now i will have to cut and paste each row or only consecutive rows.