The question is more complex than some other analyses would have it.
When you receive a work created by some other person(s), A, and you make changes, B, leading to C (which is a derivative work of both A and B), there are a number of licences to consider.
The licence under which you received A continues to apply to A, when distributed simply as A; you have no power to vary that.
You may licence B under whatever terms you please, provided that they don't cause C to be under a licence which conflicts with the licence terms on A as regard derivative works.
C, being a work in its own right, is also covered by a licence. The choice of this licence may be constrained by the licences on A or B, or it may not be. Unless so constrained to be, it is possible that C's licence will not be the same as either that on A or B.
So, if A is covered by the X11 license (the FSF note that the term "the MIT license" is ambiguous, as there have been many), you may release B under the X11 license, and C will then very likely be under the X11 licence, unless you arrange otherwise. You may release B under the GPL, in which case C will also need to be under the GPL (per GPL2 s2b or GPL3 s5c, as appropriate). You may release B under either 3- or 4-clause BSD, in which case you will need to clarify what licence C is released under.
If A is covered by the GPL, you may release B under the same version of the GPL, or under a less-restrictive licence compatible with the GPL in question (which includes 3-clause BSD, but not 4-clause BSD). C will need to be under the GPL (see previous para).
Note that this analysis is currently thought to be persuasive in England and Wales (ie, I have taken legal advice that the line of analysis is likely to find favour with a court). I have no idea whatsoever if it would find favour in other jurisdictions, but you don't say where you're based. IANAL/IANYL, of course.