Is it a good/acceptable practice to combine checkboxes with radio buttons for one question?

I work on a form, in which there are questions allowing either multiple choices or selecting just one. An example:

Which of the sweeties do you like:

  • [ ] chocolate
  • [ ] lollipops
  • [ ] cookies
  • ( ) none

In the above, [ ] represent checkboxes and ( ) represents radiobuttons. User can select multiple sweeties, but upon selecting "none" all the checkbox fields should be cleared, and vice versa: when "none" is selected, selecting any of the checkboxes should clear the radio in "none".

From UX perspective, is it ok to follow this way?

Edit:

Just to clarify: "None" does not mean "none of the above". Instead, it means that user does not like sweeties at all. In other words: the options included as checkboxes are just a subset of all possible sweeties. User can choose one/multiple of the sweeties or select "none". One conclusion is that the form does not cover a situation when user likes other sweeties than the ones listed as options, so definitely the form should also include "Other, please specify:" field as well.

Edit:

Ha! After 2 years I found it here:

User Experience Research Studies registration form

So at least I am not alone in my belief that this is the right way to do it.