Such a deep number

Since there are so many mathematical constants that I love, I decided to make one of my own. Since I love primes and my favorite prime number is 19, I chose to go with it for this problem. My constant was the square root of 19 which comes out to be (obviously irrational )

$\sqrt{19} = 4.35889894354067\ldots.$

Obviously, I am not a mathematician, I am crazy and I like to play with numbers, so I decided to go with the following approximation for the square root of 19:

$\sqrt{19} \approx 4.3588989.$

which, to be clear is a rational number .

I then decided to play a little bit more and express this rational number in the form of its continued fraction ,

$4.3588989 = 4+\cfrac{1}{a+\cfrac{1}{b+\cfrac{1}{c+\cfrac{1}{d+\cfrac{1}{e+\cfrac{1}{f+\cfrac{1}{g+\cfrac{1}{h+\cfrac{1}{i+\cfrac{1}{j+\cfrac{1}{k+\cfrac{1}{l+\cfrac{1}{m+\cfrac{1}{n+\cfrac{1}{o+\cfrac{1}{p+\cfrac{1}{q}}}}}}}}}}}}}}}}}$

I have hidden all the numbers for this problem by the symbols $a,b,c,\ldots,p,q$ , all of which are positive integers.

Find the sum of all these symbols, $a+b+c+d+\cdots+o+p+q$ .