1. **State the problem:** Simplify the expression $$(5x^3 - 6x + 10) + (x^3 + 10x - 9)$$. 2. **Combine like terms:** Group the terms with the same powers of $x$ together. $$5x^3 + x^3 - 6x + 10x + 10 - 9$$ 3. **Add coefficients of like terms:** $$ (5 + 1)x^3 + (-6 + 10)x + (10 - 9) $$ 4. **Simplify each term:** $$ 6x^3 + 4x + 1 $$ 5. **Final answer:** $$6x^3 + 4x + 1$$ This is the simplified form of the given expression.