It shouldn't be dangerous no.
You can expect some fairly heavy sedation by combining the two. There shouldn't be any danger from respiratory depression, as this is not a primary effect of Dextromethorphan (DXM). Respiratory depression is generally what you're worried about when Opioids are involved, so i say have at it.
Dextromethorphan and Methadone are chemically related. They're like first or second cousins.
Opioids are known for their analgesic effects. Historically, the antitussive effects have also been very useful. Dextromethorphan came on the scene as a drug aiming to capitalize on the antitussive effects of Opioids, without the associated risks of addiction, impairment, tolerance etc.
Dextromethorphan is on half of the chiral substance "Methorphan" or "Racemethorphan" as it is sometimes called. The mirror image of this Dextromethorphan is Levomethorphan, which is actually a fairly potent Opioid that never saw clinical use in America at least.
In that same way, Methadone is a chiral molecule.
Levomethadone is a potent Opioid agonist, while Dextromethadone is essentially analogous to the Dextromethorphan that we are talking about now. Dextromethadone is also a fairly effective antitussive. To my knowledge, similarly high doses of Dextromethadone would cause similar effects to Dextromethorphan.
This is how they are related. I thought you might find this interesting.