The expression \( (x^3+6x^2)-(5x^2+12x) \) can be rewritten as \( (x+a)(x+b)(x+c) \), where \(a,b,\) and \(c\) are constants. What is the value of \(a+b+c\)?

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We want to expand and convert the polynomial into its factored form.

$$(x^3+6x^2)-(5x^2+12x) $$ $$ =x^3+6x^2-5x^2-12x $$ $$ =x^3+x^2-12x $$ $$ =x(x^2+x-12) $$ $$ =x(x+4)(x-3) $$

Comparing this expression to \( (x+a)(x+b)(x+c) \),

$$a=0, b=4, c=-3 $$ $$ a+b+c= $$ $$ 0+4-3=\boxed{1}$$