Fortunately you don't need to edit the shortcode manually. When you edit the gallery by adding another image using the WordPress Media interface, the shortcode gets modified automatically.
Let's use this example. Say you have two posts that have three attached images each. Post 1 has attachment 100, 101 and 102. Post 2 has attachment 103, 104, and 105. You merge them into a single gallery using the shortcode:
[gallery id="1,2"]
Then you decide that you want to add one image that is not attached to either post. Let's assume this image has an id of 200. All you would need to do is edit the post and make sure that the content view was set to "Visual", then click the "Edit Gallery" link on the gallery placeholder.
When the Edit Gallery window appears, select "Add to Gallery" in the left sidebar. Then select the image(s) you want added to the gallery. Click the "Add to Gallery" button at the bottom-right of the window, then click "Update Gallery".
The next time you switch to "Text" mode when viewing the content, you will see the gallery shortcode has been transformed like so:
[gallery ids="100,101,102,103,104,105,200" id="1,2"]
Note that the "id" argument has no bearing on the gallery output when the "ids" argument is present. The beauty of this solution is that you could easily return to the original merged gallery by editing the shortcode and removing the "ids" argument.
We hope that this clarifies the approach to the solution. Let us know if it does not.