Javascript, 3232 39 bytes
s=>eval((s.match(/\d+/g)||[0]).join`+`)
f=
s=>eval((s.match(/\d+/g)||[0]).join`+`)
F=s=>document.body.innerHTML+='<pre>f(\''+s+'\') -> '+f(s)+'\n</pre>'
F('a')
F('5')
F('10')
F('1a1')
F('11a1')
F('4dasQWE65asAs5dAa5dWD')
F('a1wAD5qw45REs5Fw4eRQR33wqe4WE')