HTTP error occurred during file upload (404: File not found) when uploading images to CKEditor with KCFinder

Question

I've installed ckeditor and kcfinder in my /public directory. Despite having added to /public/ckeditor/config.js:

config.filebrowserBrowseUrl = '/kcfinder/browse.php?opener=ckeditor&type=files';
config.filebrowserImageBrowseUrl = '/kcfinder/browse.php?opener=ckeditor&type=images';
config.filebrowserFlashBrowseUrl = '/kcfinder/browse.php?opener=ckeditor&type=flash';

config.filebrowserUploadUrl = '/kcfinder/upload.php?opener=ckeditor&type=files';
config.filebrowserImageUploadUrl = '/kcfinder/upload.php?opener=ckeditor&type=images';
config.filebrowserFlashUploadUrl = '/kcfinder/upload.php?opener=ckeditor&type=flash';

and enabled KCFinder in /public/kcfinder/config.php

'disabled' => false,
'uploadURL' => "/uploads",
// The uploads directory is inside /public

I got an error trying to upload images to CKEditor.

HTTP error occurred during file upload (404: File not found).

I've noticed some errors in my console

[CKEDITOR] Error code: cloudservices-no-token-url.
[CKEDITOR] Error code: cloudservices-no-upload-url.