Bring a large pot of salted water to a boil and cook the spaghetti according to package directions until al dente; drain and set aside.
Heat the large nonstick skillet over medium-high heat. Add the ground beef and cook, breaking it up with a spoon, until no longer pink, about 5–7 minutes; drain any excess fat.
Sprinkle the taco seasoning over the cooked beef and pour in 2/3 cup water; stir and cook over medium-high heat for 2–3 minutes until the seasoning is incorporated.
Stir in the tomato paste, undrained Rotel, and condensed cream of chicken soup. Add the cubed Velveeta and shredded cheddar; reduce heat to medium and cook, stirring, until all the cheese is melted and the sauce is smooth.
Add the drained spaghetti and rinsed black beans to the skillet; toss gently to coat the pasta in the sauce and heat through.
Sprinkle with chopped cilantro, if using, and serve immediately.