Let's solve the expression step by step.
Start with the innermost operations, in this case, the division and multiplication:
- \( 1835 \div 5 = 367 \)
- \( 97 \times 6 = 582 \)
Substitute these values back into the expression: \[ (765 + 367 - 582) \cdot 3 \]
Now perform the addition and subtraction inside the parentheses:
- \( 765 + 367 = 1132 \)
- \( 1132 - 582 = 550 \)
Now substitute this result back into the expression: \[ 550 \cdot 3 \]
Finally, perform the multiplication:
- \( 550 \cdot 3 = 1650 \)
Thus, the value of the expression \( (765 + 1835 \div 5 - 97 \cdot 6) \cdot 3 \) is \( \boxed{1650} \).