The Sixth Amendment applies to everyone living in the US.
It does, however, the Constitutional interpretation of that right is *not* defined in a clearcut manner.
The primary precedent on this matter is the 1972 Supreme Court ruling in
Barker v. Wingo, a case in which a man's murder trial was delayed for over five years because the prosecution wanted to first convict his alleged accomplice. Because the case against the accomplice was weak, he was tried
six times before finally being found guilty, and then the trial was
even further delayed by the lengthy illness of a key witness.
The Court of Appeals ruled that the defendant had waived his right to a speedy trial because he had not objected to the first eleven continuances granted to the prosecution, because the clock for a "speedy trial" did not start ticking until the defendant actually objected to a continuance, and that had only been eight months before trial.
(Note that the Court of Appeals made a serious factual error here, ruling that it had only been eight months from Barker's first objection to his actual trial, when it had in fact been twenty months.)
SCOTUS upheld the Court of Appeals ruling, with three key points to the precedent:
1. The right to a speedy trial is "generically different" from other Constitutional rights because it is not purely an individual right, but a right that was created for the greater good of society and the justice system as a whole.
2. There is no way to create a "firm distinction" between what is and is not a speedy trial, because every trial has unique circumstances.
3. Whether or not the right to a speedy trial has been violated requires a "balancing test" of four key factors: the length of the delay, the reason for the delay, the defendant's assertion of the right, and prejudice towards the defendant*.
*note that this is a legal jargon use of the term "prejudice" -- it is not saying that minority defendants are entitled to extra speediness, but that the courts must consider how much the delay in trial has negatively affected the defendant's life/case. A defendant who had been held in jail for years awaiting trial has suffered greater "prejudice towards the defendant" than a defendant who was out on bail for the same period.